CANTOR'S TWO PROOFS
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From: |-|ercules on 17 Jun 2010 20:27 You blame me for an argumentative error by declining to answer my clarification question. You also don't follow my simple assertion that your definition of your new real is identical to your proof that your new real is different. Yes I know AD(n) =/= L(n,n) -> AD(n) =/= L(n,n) I know that it's only the FINITE sequences of digits that are KNOWN to be computable, I'm not saying this directly implies the INFINITE sequences are all computable, I'm saying that you cannot produce a unique pattern of digits. Your 0.1, 0.2, .., 0.3, counter example is meaningless. It's a quantitative difference, you still have to show a qualitative pattern of new digits. And no I can easily define a bijection to a powerset, it's just the computable subsets. It's an oxymoron to think a computer will miss some subset of naturals. It's a trivial exercise. Anyway we are done, everyone is refusing to answer my simple questions and still have the nerve to keep repeating CANTOR PROVED... Herc
From: rick_s on 19 Jun 2010 10:03
In article <87tjn9Fg79U1(a)mid.individual.net>, radgray123(a)yahoo.com says... > > >CANTOR'S POWER PROOF! >Superinfinity is based on the circular reasoning >"no box contains the box numbers that don't contain their own box number". Who shaves the barber if the barber shaves everyone who does not shave themselves? > >No I don't like it either but there is a new sequence because we *construct* it like so: > >CANTORS DIFFERENT PROOF! >Defn: digit 1 is different, and digit 2 is different, digit 3 is different, .... >Proof: digit 1 is different, and digit 2 is different, digit 3 is different... >Therefore it's a different number! The idea of infinity is that it never ends. So it has to be undefined since it is never in the spot where it has the focus on it as a real object, since it is a potential value not a real value. It goes on potentially forever. However, if you look at it in the abstract form, and you substitute goats and chickens, then you can do math with the goats and chickens and it will end up the same. If you are saying that a goat shall represent a type of infinity. Then if you said another type of infinity is also a goat, and now I can do math on the goats, and say I have two goats or one goat take away one goat is no goats, and in that same logical framework, I can objectify the infinities so as to treat them as objects. (is it real math though or another one of those squaree root of minus 1 deals?) |